Subgroups — #12064954

Order 1280.

836 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10611013	C₂	1	1	yes	maximal, characteristic
2	D₅×#431	C₂	1	1	yes	maximal, characteristic
3	C₄×D₅×M₁₆	C₂	1	1	yes	maximal, characteristic
4	C₅×#1453	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601536	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601536	C₂	1	1	yes	maximal, characteristic, complemented
7	#10600641	C₂	1	1	yes	maximal, characteristic, complemented
8	#10598863	C₂	1	1	yes	maximal, characteristic, complemented
9	#10598863	C₂	1	1	yes	maximal, characteristic, complemented
10	#10598862	C₂	1	1	yes	maximal, characteristic, complemented
11	#10598862	C₂	1	1	yes	maximal, characteristic, complemented
12	#10598860	C₂	1	1	yes	maximal, characteristic, complemented
13	#10598860	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×#676	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×#676	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₅×M₁₆	C₄	1	2	yes	—
17	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic
18	C₅×#431	C₂²	1	1	yes	characteristic
19	C₅×#431	C₂²	1	1	yes	characteristic
20	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
21	M₁₆×Dic₅	C₄	1	2	yes	—
22	#65214	C₂²	1	1	yes	characteristic
23	#65214	C₂²	1	1	yes	characteristic
24	C₄×#681	C₂²	1	1	yes	characteristic
25	#65126	C₄	1	2	yes	—
26	#65124	C₄	1	2	yes	—
27	#65122	C₄	1	2	yes	—
28	D₅×C₄⋊C₈	C₄	1	2	yes	—
29	#65015	C₄	1	2	yes	—
30	D₅×C₂²⋊C₈	C₄	1	2	yes	—
31	#65008	C₄	1	2	yes	—
32	#65007	C₄	1	2	yes	—
33	#64996	C₄	1	2	yes	—
34	D₅×#97	C₄	1	2	yes	—
35	C₄×#676	C₂²	1	1	yes	characteristic
36	C₄×#676	C₂²	1	1	yes	characteristic
37	C₄×#676	C₂²	1	1	yes	characteristic
38	C₄×#676	C₂²	1	1	yes	characteristic
39	#64974	C₂²	1	1	yes	characteristic
40	#64974	C₂²	1	1	yes	characteristic
41	#64974	C₂²	1	1	yes	characteristic
42	#64974	C₂²	1	1	yes	characteristic
43	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
44	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
45	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
47	C₅×#322	C₂²	1	1	yes	characteristic, complemented
48	C₅×#322	C₂²	1	1	yes	characteristic, complemented
49	C₅×#322	C₂²	1	1	yes	characteristic, complemented
50	C₅×C₈²	C₂²	1	1	yes	characteristic, complemented
51	#64675	C₂²	1	1	yes	characteristic, complemented
52	#64675	C₂²	1	1	yes	characteristic, complemented
53	#64675	C₂²	1	1	yes	characteristic, complemented
54	#64674	C₂²	1	1	yes	characteristic, complemented
55	#64674	C₂²	1	1	yes	characteristic, complemented
56	#64674	C₂²	1	1	yes	characteristic, complemented
57	#64674	C₂²	1	1	yes	characteristic, complemented
58	#64674	C₂²	1	1	yes	characteristic, complemented
59	#64674	C₂²	1	1	yes	characteristic, complemented
60	C₈×#168	C₂²	1	1	yes	characteristic, complemented
61	C₈×#168	C₂²	1	1	yes	characteristic, complemented
62	C₈×#168	C₂²	1	1	yes	characteristic, complemented
63	#17327	—	5	1	no	maximal, Sylow
64	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
67	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
68	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
69	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
72	C₂×#681	C₂×C₄	1	2	yes	—
73	D₅×M₁₆	—	2	8	no	—
74	C₂×#676	C₂×C₄	1	2	yes	—
75	C₂×#676	C₂×C₄	1	2	yes	—
76	C₂×#676	C₂×C₄	1	2	yes	—
77	C₂×#676	C₂×C₄	1	2	yes	—
78	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
79	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
80	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
81	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
82	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
83	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
84	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
85	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
86	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
87	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
88	C₄²×D₅	C₂³	1	1	yes	characteristic
89	C₄²×D₅	C₂³	1	1	yes	characteristic
90	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
91	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
92	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
93	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
94	C₅×#97	C₂×C₄	1	2	yes	—
95	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
96	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
97	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
98	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
99	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
100	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
101	C₂²⋊#168	C₂×C₄	1	2	yes	—
102	C₂²⋊#168	C₂×C₄	1	2	yes	—
103	#3952	C₂×C₄	1	2	yes	—
104	#3952	C₂×C₄	1	2	yes	—
105	#3952	C₂×C₄	1	2	yes	—
106	#3952	C₂×C₄	1	2	yes	—
107	#3947	C₂×C₄	1	2	yes	—
108	#3947	C₂×C₄	1	2	yes	—
109	#3947	C₂×C₄	1	2	yes	—
110	#3947	C₂×C₄	1	2	yes	—
111	#3946	C₂×C₄	1	2	yes	—
112	#3946	C₂×C₄	1	2	yes	—
113	#3946	C₂×C₄	1	2	yes	—
114	#3946	C₂×C₄	1	2	yes	—
115	C₈×Dic₅	C₂×C₄	1	2	yes	—
116	C₈×Dic₅	C₂×C₄	1	2	yes	—
117	C₈×Dic₅	C₂×C₄	1	2	yes	—
118	C₈×Dic₅	C₂×C₄	1	2	yes	—
119	C₄⋊#168	C₂×C₄	1	2	yes	—
120	C₄⋊#168	C₂×C₄	1	2	yes	—
121	#3935	C₂×C₄	1	2	yes	—
122	C₄×#168	C₂³	1	1	yes	characteristic
123	C₄×#168	C₂³	1	1	yes	characteristic
124	C₄×#168	C₂³	1	1	yes	characteristic
125	C₄×#168	C₂³	1	1	yes	characteristic
126	C₄×#168	C₂³	1	1	yes	characteristic
127	C₄×#168	C₂³	1	1	yes	characteristic
128	#2920	—	5	1	no	—
129	C₂×#431	—	5	1	no	—
130	C₂×C₄×M₁₆	—	5	1	no	—
131	#1453	—	5	1	no	—
132	#1453	—	5	1	no	—
133	#1453	—	5	1	no	—
134	#1453	D₅	1	1	yes	characteristic, complemented
135	#1451	—	5	1	no	—
136	#1451	—	5	1	no	—
137	#1451	—	5	1	no	—
138	#1451	—	5	1	no	—
139	C₈×M₁₆	—	5	1	no	—
140	C₈×M₁₆	—	5	1	no	—
141	C₈×M₁₆	—	5	1	no	—
142	C₈×M₁₆	—	5	1	no	—
143	C₂³×D₅	C₄²	1	1	yes	characteristic
144	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
147	C₂²×Dic₅	C₄²	1	1	yes	characteristic
148	C₂²×Dic₅	C₄²	1	1	yes	characteristic
149	C₂²×Dic₅	C₄²	1	1	yes	characteristic
150	C₂×C₄×D₅	—	2	4	no	—
151	C₂×C₄×D₅	—	2	4	no	—
152	C₂×C₄×D₅	—	4	2	no	—
153	C₂×C₄×D₅	C₄²	1	1	yes	characteristic
154	C₂×C₄×D₅	C₄²	1	1	yes	characteristic
155	C₂×C₄×D₅	C₄²	1	1	yes	characteristic
156	C₂×C₄×D₅	C₄²	1	1	yes	characteristic
157	C₂×C₄×D₅	C₄²	1	1	yes	characteristic
158	C₂×C₄×D₅	C₄²	1	1	yes	characteristic
159	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
165	C₅×M₁₆	—	2	4	no	—
166	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
167	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
168	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
169	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
170	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
171	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
172	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
173	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
174	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
175	C₄²×C₅	C₂⁴	1	1	yes	characteristic
176	C₄×Dic₅	C₄²	1	1	yes	characteristic
177	C₄×Dic₅	C₄²	1	1	yes	characteristic
178	C₄×Dic₅	C₄²	1	1	yes	characteristic
179	C₄×Dic₅	C₄²	1	1	yes	characteristic
180	C₄×Dic₅	C₄²	1	1	yes	characteristic
181	C₄×Dic₅	C₄²	1	1	yes	characteristic
182	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
183	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
184	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
185	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
186	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
187	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
188	#681	—	2	4	no	—
189	C₂×#168	C₂²×C₄	1	2	yes	—
190	C₂×#168	C₂²×C₄	1	2	yes	—
191	C₂×#168	C₂²×C₄	1	2	yes	—
192	C₂×#168	C₂²×C₄	1	2	yes	—
193	C₂×#168	C₂²×C₄	1	2	yes	—
194	C₂×#168	C₂²×C₄	1	2	yes	—
195	#676	—	2	4	no	—
196	#676	—	2	4	no	—
197	#676	—	2	4	no	—
198	#676	M₁₆	1	8	yes	complemented
199	C₈×D₅	—	2	4	no	—
200	C₈×D₅	—	2	4	no	—
201	C₈×D₅	—	4	2	no	—
202	C₈×D₅	—	4	2	no	—
203	C₂²×M₁₆	—	5	2	no	—
204	C₂²×C₄²	—	5	1	no	—
205	#432	—	5	2	no	—
206	#432	—	5	2	no	—
207	#431	—	5	1	no	—
208	#431	—	5	1	no	—
209	#431	—	5	2	no	—
210	#431	—	5	2	no	—
211	#431	—	5	1	no	—
212	#431	—	5	1	no	—
213	#431	—	5	1	no	—
214	#431	—	5	1	no	—
215	#431	C₂×D₅	1	1	yes	characteristic
216	#431	C₂×D₅	1	1	yes	characteristic
217	#423	—	5	2	no	—
218	C₂×C₄⋊C₈	—	5	2	no	—
219	#407	—	5	2	no	—
220	C₂×C₂²⋊C₈	—	5	2	no	—
221	C₄×M₁₆	—	5	2	no	—
222	C₄×M₁₆	—	5	1	no	—
223	C₄×M₁₆	—	5	2	no	—
224	C₄×M₁₆	—	5	1	no	—
225	C₄×M₁₆	—	5	1	no	—
226	C₄×M₁₆	—	5	1	no	—
227	C₄×M₁₆	—	5	1	no	—
228	C₄×M₁₆	C₂×D₅	1	1	yes	characteristic
229	C₂×#97	—	5	2	no	—
230	C₂×C₄×C₈	—	5	1	no	—
231	C₂×C₄×C₈	—	5	1	no	—
232	C₂×C₄×C₈	—	5	1	no	—
233	C₂×C₄×C₈	—	5	1	no	—
234	#322	—	5	1	no	—
235	#322	—	5	1	no	—
236	#322	—	5	1	no	—
237	#322	—	5	1	no	—
238	#322	—	5	1	no	—
239	#322	—	5	1	no	—
240	#322	—	5	1	no	—
241	#322	—	5	1	no	—
242	#322	—	5	1	no	—
243	#322	C₂×D₅	1	1	yes	characteristic, complemented
244	#322	C₂×D₅	1	1	yes	characteristic, complemented
245	#322	C₂×D₅	1	1	yes	characteristic, complemented
246	C₈²	—	5	1	no	—
247	C₈²	—	5	1	no	—
248	C₈²	—	5	1	no	—
249	C₈²	C₂×D₅	1	1	yes	characteristic, complemented
250	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
251	C₂²×D₅	—	2	2	no	—
252	C₂²×D₅	—	2	2	no	—
253	C₂²×D₅	—	4	1	no	—
254	C₂²×D₅	C₂×C₄²	1	1	yes	characteristic
255	C₂²×D₅	C₂×C₄²	1	1	yes	characteristic
256	C₂×C₄×C₅	—	2	2	no	—
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
260	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
261	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
263	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
265	C₂×Dic₅	—	2	2	no	—
266	C₂×Dic₅	—	2	2	no	—
267	C₂×Dic₅	—	4	1	no	—
268	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
269	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
270	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
271	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
272	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
273	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
274	C₄×D₅	—	2	2	no	—
275	C₄×D₅	—	2	2	no	—
276	C₄×D₅	—	2	2	no	—
277	C₄×D₅	—	2	2	no	—
278	C₄×D₅	—	2	2	no	—
279	C₄×D₅	—	2	2	no	—
280	C₄×D₅	—	2	2	no	—
281	C₄×D₅	—	2	2	no	—
282	C₄×D₅	—	4	1	no	—
283	C₄×D₅	—	4	1	no	—
284	C₄×D₅	C₂×M₁₆	1	4	yes	—
285	C₄×D₅	#131	1	4	yes	—
286	C₅×C₈	—	2	2	no	—
287	C₅×C₈	—	2	2	no	—
288	C₅×C₈	—	2	2	no	—
289	C₅×C₈	—	2	2	no	—
290	C₅×C₈	—	2	2	no	—
291	C₅×C₈	C₂×M₁₆	1	4	yes	—
292	#168	—	2	2	no	—
293	#168	—	2	2	no	—
294	#168	—	2	2	no	—
295	#168	—	2	2	no	—
296	#168	—	2	2	no	—
297	#168	C₂×M₁₆	1	4	yes	—
298	C₂³×C₄	—	5	1	no	—
299	C₂³×C₄	—	5	1	no	—
300	C₂³×C₄	—	5	1	no	—
301	C₂×M₁₆	—	5	2	no	—
302	C₂×M₁₆	—	5	2	no	—
303	C₂×M₁₆	—	5	2	no	—
304	C₂×M₁₆	—	5	2	no	—
305	C₂×M₁₆	—	5	2	no	—
306	C₂×M₁₆	—	10	8	no	—
307	C₂×M₁₆	C₄×D₅	1	2	yes	—
308	C₂²×C₈	—	5	2	no	—
309	C₂²×C₈	—	5	2	no	—
310	C₂²×C₈	—	5	2	no	—
311	C₂²×C₈	—	5	2	no	—
312	C₂×C₄²	—	5	1	no	—
313	C₂×C₄²	—	5	1	no	—
314	C₂×C₄²	—	5	1	no	—
315	C₂×C₄²	—	5	1	no	—
316	C₂×C₄²	—	5	1	no	—
317	C₂×C₄²	—	5	1	no	—
318	C₂×C₄²	—	5	1	no	—
319	C₂×C₄²	—	5	1	no	—
320	C₂×C₄²	—	5	1	no	—
321	C₂×C₄²	—	5	1	no	—
322	C₂×C₄²	—	5	1	no	—
323	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
324	C₄⋊C₈	—	5	2	no	—
325	C₄⋊C₈	—	5	2	no	—
326	C₄⋊C₈	—	5	2	no	—
327	C₄⋊C₈	—	5	2	no	—
328	C₄⋊C₈	—	5	2	no	—
329	C₄⋊C₈	—	5	2	no	—
330	C₄⋊C₈	C₄×D₅	1	2	yes	—
331	C₄⋊C₈	C₄×D₅	1	2	yes	—
332	C₂²⋊C₈	—	5	2	no	—
333	C₂²⋊C₈	—	5	2	no	—
334	C₂²⋊C₈	—	5	2	no	—
335	C₂²⋊C₈	—	5	2	no	—
336	C₂²⋊C₈	—	5	2	no	—
337	C₂²⋊C₈	—	5	2	no	—
338	C₂²⋊C₈	C₄×D₅	1	2	yes	—
339	C₂²⋊C₈	C₄×D₅	1	2	yes	—
340	#97	—	5	2	no	—
341	#97	—	5	2	no	—
342	#97	—	5	2	no	—
343	#97	—	5	2	no	—
344	#97	—	5	2	no	—
345	#97	C₄×D₅	1	2	yes	—
346	C₄×C₈	—	5	2	no	—
347	C₄×C₈	—	5	2	no	—
348	C₄×C₈	—	5	2	no	—
349	C₄×C₈	—	5	2	no	—
350	C₄×C₈	—	5	1	no	—
351	C₄×C₈	—	5	1	no	—
352	C₄×C₈	—	5	1	no	—
353	C₄×C₈	—	5	1	no	—
354	C₄×C₈	—	5	1	no	—
355	C₄×C₈	—	5	1	no	—
356	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
357	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
358	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
359	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
360	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
361	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
362	C₂²×C₅	—	2	1	no	—
363	C₂²×C₅	—	2	1	no	—
364	C₂²×C₅	—	2	1	no	—
365	C₂²×C₅	C₂²×C₄²	1	1	yes	characteristic
366	C₂×D₅	—	2	1	no	—
367	C₂×D₅	—	2	1	no	—
368	C₂×D₅	—	2	1	no	—
369	C₂×D₅	—	2	1	no	—
370	C₂×D₅	—	4	4	no	—
371	C₂×D₅	C₄×M₁₆	1	2	yes	—
372	C₂×D₅	#405	1	2	yes	—
373	C₄×C₅	—	2	1	no	—
374	C₄×C₅	—	2	1	no	—
375	C₄×C₅	—	2	1	no	—
376	C₄×C₅	C₂²×M₁₆	1	2	yes	—
377	C₄×C₅	C₂×#131	1	2	yes	—
378	C₄×C₅	#568	1	2	yes	—
379	Dic₅	—	2	1	no	—
380	Dic₅	—	2	1	no	—
381	Dic₅	—	2	1	no	—
382	Dic₅	—	2	1	no	—
383	Dic₅	C₄×M₁₆	1	2	yes	—
384	Dic₅	#405	1	2	yes	—
385	C₂⁴	—	5	1	no	—
386	C₂²×C₄	—	5	1	no	—
387	C₂²×C₄	—	5	1	no	—
388	C₂²×C₄	—	5	1	no	—
389	C₂²×C₄	—	5	1	no	—
390	C₂²×C₄	—	5	1	no	—
391	C₂²×C₄	—	5	1	no	—
392	C₂²×C₄	—	5	1	no	—
393	C₂²×C₄	—	5	1	no	—
394	C₂²×C₄	—	5	1	no	—
395	C₂²×C₄	—	5	1	no	—
396	C₂²×C₄	—	5	1	no	—
397	C₂²×C₄	—	5	1	no	—
398	C₂²×C₄	—	5	1	no	—
399	C₂²×C₄	—	5	1	no	—
400	C₂²×C₄	—	5	1	no	—
401	C₂²×C₄	—	10	4	no	—
402	C₂²×C₄	—	10	4	no	—
403	C₂²×C₄	—	20	2	no	—
404	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
405	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
406	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
407	M₁₆	—	2	4	no	—
408	M₁₆	—	5	8	no	—
409	M₁₆	—	10	4	no	—
410	M₁₆	—	10	4	no	—
411	M₁₆	—	10	4	no	—
412	M₁₆	—	10	4	no	—
413	C₂×C₈	—	5	2	no	—
414	C₂×C₈	—	5	2	no	—
415	C₂×C₈	—	5	2	no	—
416	C₂×C₈	—	5	2	no	—
417	C₂×C₈	—	5	2	no	—
418	C₂×C₈	—	5	2	no	—
419	C₂×C₈	—	10	4	no	—
420	C₂×C₈	—	10	4	no	—
421	C₂×C₈	—	20	2	no	—
422	C₂×C₈	—	20	2	no	—
423	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
424	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
425	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
426	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
427	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
428	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
429	C₄²	—	5	1	no	—
430	C₄²	—	5	1	no	—
431	C₄²	—	5	1	no	—
432	C₄²	—	5	1	no	—
433	C₄²	—	5	1	no	—
434	C₄²	—	5	1	no	—
435	C₄²	—	5	1	no	—
436	C₄²	—	5	1	no	—
437	C₄²	—	5	1	no	—
438	C₄²	—	5	1	no	—
439	C₄²	—	5	1	no	—
440	C₄²	—	5	1	no	—
441	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
442	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
443	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
444	C₄²	C₂³×D₅	1	1	yes	characteristic
445	C₂×C₅	—	4	1	no	—
446	C₂×C₅	C₂×C₄×M₁₆	1	1	yes	characteristic
447	C₂×C₅	C₂×#405	1	1	yes	characteristic
448	C₂×C₅	#2873	1	1	yes	characteristic
449	D₅	—	2	2	no	—
450	D₅	—	2	2	no	—
451	C₂³	—	5	1	no	—
452	C₂³	—	5	1	no	—
453	C₂³	—	10	2	no	—
454	C₂³	—	10	2	no	—
455	C₂³	—	20	1	no	—
456	C₂³	C₄²×D₅	1	1	yes	characteristic
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	5	1	no	—
461	C₂×C₄	—	5	1	no	—
462	C₂×C₄	—	5	4	no	—
463	C₂×C₄	—	5	4	no	—
464	C₂×C₄	—	5	1	no	—
465	C₂×C₄	—	5	1	no	—
466	C₂×C₄	—	5	1	no	—
467	C₂×C₄	—	5	1	no	—
468	C₂×C₄	—	10	2	no	—
469	C₂×C₄	—	10	2	no	—
470	C₂×C₄	—	10	2	no	—
471	C₂×C₄	—	10	2	no	—
472	C₂×C₄	—	10	2	no	—
473	C₂×C₄	—	10	2	no	—
474	C₂×C₄	—	10	2	no	—
475	C₂×C₄	—	10	2	no	—
476	C₂×C₄	—	10	2	no	—
477	C₂×C₄	—	10	2	no	—
478	C₂×C₄	—	20	1	no	—
479	C₂×C₄	—	20	1	no	—
480	C₂×C₄	—	20	1	no	—
481	C₂×C₄	C₄²×D₅	1	1	yes	characteristic
482	C₂×C₄	C₄²×D₅	1	1	yes	characteristic
483	C₂×C₄	C₄²×D₅	1	1	yes	characteristic
484	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
485	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
486	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
487	C₈	—	2	2	no	—
488	C₈	—	2	2	no	—
489	C₈	—	2	2	no	—
490	C₈	—	2	2	no	—
491	C₈	—	2	2	no	—
492	C₈	—	5	4	no	—
493	C₈	—	10	2	no	—
494	C₈	—	10	2	no	—
495	C₈	—	10	2	no	—
496	C₈	—	10	2	no	—
497	C₈	—	10	2	no	—
498	C₈	D₅×M₁₆	1	4	yes	—
499	C₅	#17327	1	1	yes	characteristic, complemented, Sylow
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	5	2	no	—
504	C₂²	—	5	2	no	—
505	C₂²	—	10	1	no	—
506	C₂²	—	10	1	no	—
507	C₂²	—	10	1	no	—
508	C₂²	—	10	1	no	—
509	C₂²	—	20	4	no	—
510	C₂²	C₂×C₄²×D₅	1	1	yes	characteristic
511	C₄	—	2	1	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	5	2	no	—
515	C₄	—	5	2	no	—
516	C₄	—	10	1	no	—
517	C₄	—	10	1	no	—
518	C₄	—	10	1	no	—
519	C₄	—	10	1	no	—
520	C₄	C₂×D₅×M₁₆	1	2	yes	—
521	C₄	D₅×#131	1	2	yes	—
522	C₄	#66084	1	2	yes	—
523	C₂	—	4	1	no	—
524	C₂	—	10	2	no	—
525	C₂	—	10	2	no	—
526	C₂	C₄×D₅×M₁₆	1	1	yes	characteristic
527	C₂	D₅×#405	1	1	yes	characteristic
528	C₂	#10610279	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₅
commutator, socle	C₂²×C₅	C₂²×C₄²
Fitting	C₅×#1453	C₂
prime radical	C₂³×D₅	C₄²
cosocle	C₄²×C₅	C₂⁴
hypercenter	#1453	D₅
hypocenter	C₅	#17327
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₄² ◁ #1453

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. C₅×#1453	C₂	semidirect
5. #10601536	C₂	semidirect
6. #10601536	C₂	semidirect
7. #10600641	C₂	semidirect
8. #10598863	C₂	semidirect
9. #10598863	C₂	semidirect
10. #10598862	C₂	semidirect
11. #10598862	C₂	semidirect
12. #10598860	C₂	semidirect
13. #10598860	C₂	semidirect
14. C₈×#676	C₂	semidirect
15. C₈×#676	C₂	semidirect
47. C₅×#322	C₂²	semidirect
48. C₅×#322	C₂²	semidirect
49. C₅×#322	C₂²	semidirect
50. C₅×C₈²	C₂²	semidirect
51. #64675	C₂²	semidirect
52. #64675	C₂²	semidirect
53. #64675	C₂²	semidirect
54. #64674	C₂²	semidirect
55. #64674	C₂²	semidirect
56. #64674	C₂²	semidirect
57. #64674	C₂²	semidirect
58. #64674	C₂²	semidirect
59. #64674	C₂²	semidirect
60. C₈×#168	C₂²	semidirect
61. C₈×#168	C₂²	semidirect
62. C₈×#168	C₂²	semidirect
134. #1453	D₅	semidirect
198. #676	M₁₆	semidirect
243. #322	C₂×D₅	semidirect
244. #322	C₂×D₅	semidirect
245. #322	C₂×D₅	semidirect
249. C₈²	C₂×D₅	semidirect
499. C₅	#17327	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#10611013	2
D₅×#431	2
C₄×D₅×M₁₆	2
C₅×#1453	2
#10601536	2
#10600641	2
#10598863	2
#10598862	2
#10598860	2
C₈×#676	2
#17327	5